Solve 350*14/sqrt{14^2+5^2+6^2}

$$350 \times \frac { 14 } { \sqrt { 14 ^ { 2 } + 5 ^ { 2 } + 6 ^ { 2 } } }$$

Evaluate

$$\frac{4900\sqrt{257}}{257}\approx 305.65360216$$

Solution Steps

Calculate 14 to the power of 2 and get 196.

$$350\times \frac{14}{\sqrt{196+5^{2}+6^{2}}}$$

Calculate 5 to the power of 2 and get 25.

$$350\times \frac{14}{\sqrt{196+25+6^{2}}}$$

Add 196 and 25 to get 221.

$$350\times \frac{14}{\sqrt{221+6^{2}}}$$

Calculate 6 to the power of 2 and get 36.

$$350\times \frac{14}{\sqrt{221+36}}$$

Add 221 and 36 to get 257.

$$350\times \frac{14}{\sqrt{257}}$$

Rationalize the denominator of \frac{14}{\sqrt{257}} by multiplying numerator and denominator by \sqrt{257}.

$$350\times \frac{14\sqrt{257}}{\left(\sqrt{257}\right)^{2}}$$

The square of \sqrt{257} is 257.

$$350\times \frac{14\sqrt{257}}{257}$$

Express 350\times \frac{14\sqrt{257}}{257} as a single fraction.

$$\frac{350\times 14\sqrt{257}}{257}$$

Multiply 350 and 14 to get 4900.

$$\frac{4900\sqrt{257}}{257}$$